Frechet and Mordukhovich Derivative (Coderivative) and Covering Constant for Single-Valued Mapping in Euclidean Space with Application (II)

2025/08/14 by Li, Jinlu
#47H10 #49J52 #49J53 #90C31 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2508.11118

Abstract

We continue the study in part I for calculating the Frechet derivatives and Mordukhovich derivatives (coderivatives) and covering constants for single-valued mappings in Euclidean spaces (It is part I). In this paper, we particularly consider a norm-reserved mapping f: R² to R² that is defined by (1.1) in Section 1. We will find the precise solutions of Frechet derivative and Mordukhovich derivative at every point in R². By using these solutions, we will find the covering constant for this mapping f is exact 1 at every point in R² except the origin. Then we extend this mapping to R⁴. Finally, by using the covering constant for f and by applying the Arutyunov Mordukhovich and Zhukovskiy Parameterized Coincidence Point Theorem, we will solve some parameterized equations.

Citations

• Covering Constants for Metric Projection Operator with Applications to Stochastic Fixed-Point Problems
• Mordukhovich derivatives of the metric projection operator in uniformly convex and uniformly smooth Banach spaces
• Coincidence Points of Parameterized Generalized Equations with Applications to Optimal Value Functions

Related

• Frechet and Mordukhovich Derivative (Coderivative) and Covering Constant for Single-Valued Mapping in Euclidean Space with Applications (I)
• Calculating Covering Constants for Mappings in Euclidean Spaces Using Mordukhovich Coderivatives with Applications
• Covering Constants for Metric Projection Operator with Applications to Stochastic Fixed-Point Problems
• Differentiation and Covering Constants for Hilbert-Schmidt and Quasi-Hilbert-Schmidt Operators
• Some Applications of Arutyunov Mordukhovich Zhukovskiy Theorem to Stochastic Integral Equations